Amel Benazza-Benyahia

Building robust wavelet estimators for multicomponent images using Stein's principle

Multichannel imaging systems provide several observations of the same scene which are often corrupted by noise. In this paper, we are interested in multispectral image denoising in the wavelet domain. We adopt a multivariate statistical approach in order to exploit the correlations existing between the different spectral components. Our main contribution is the application of Steins principle to build a new estimator for arbitrary multichannel images embedded in additive Gaussian noise. Simulation tests carried out on optical satellite images show that the proposed method outperforms conventional wavelet shrinkage techniques.

A Nonlinear Stein-Based Estimator for Multichannel Image Denoising

The use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions. However, the observed images are often corrupted by an additive Gaussian noise. In this paper, we are interested in multichannel image denoising based on a multiscale representation of the images. A multivariate statistical approach is adopted to take into account both the spatial and the intercomponent correlations existing between the different wavelet subbands. More precisely, we propose a new parametric nonlinear estimator which generalizes many reported denoising methods. The derivation of the optimal parameters is achieved by applying Steins principle in the multivariate case. Experiments performed on multispectral remote sensing images clearly indicate that our method outperforms conventional wavelet denoising techniques.

A wavelet-based regularized reconstruction algorithm for SENSE parallel MRI with applications to neuroimaging

To reduce scanning time and/or improve spatial/temporal resolution in some Magnetic Resonance Imaging (MRI) applications, parallel MRI acquisition techniques with multiple coils acquisition have emerged since the early 1990s as powerful imaging methods that allow a faster acquisition process. In these techniques, the full FOV image has to be reconstructed from the resulting acquired undersampled k-space data. To this end, several reconstruction techniques have been proposed such as the widely-used SENSitivity Encoding (SENSE) method. However, the reconstructed image generally presents artifacts when perturbations occur in both the measured data and the estimated coil sensitivity profiles. In this paper, we aim at achieving accurate image reconstruction under degraded experimental conditions (low magnetic field and high reduction factor), in which neither the SENSE method nor the Tikhonov regularization in the image domain give convincing results. To this end, we present a novel method for SENSE-based reconstruction which proceeds with regularization in the complex wavelet domain by promoting sparsity. The proposed approach relies on a fast algorithm that enables the minimization of regularized non-differentiable criteria including more general penalties than a classical ℓ(1) term. To further enhance the reconstructed image quality, local convex constraints are added to the regularization process. In vivo human brain experiments carried out on Gradient-Echo (GRE) anatomical and Echo Planar Imaging (EPI) functional MRI data at 1.5T indicate that our algorithm provides reconstructed images with reduced artifacts for high reduction factors.

A SURE Approach for Digital Signal/Image Deconvolution Problems

In this paper, we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white Gaussian noise. The originality of the proposed approach is twofold. First, we formulate the restoration problem as a nonlinear estimation problem leading to the minimization of a criterion derived from Steins unbiased quadratic risk estimate. Secondly, the deconvolution procedure is performed using any analysis and synthesis frames that can be overcomplete or not. New theoretical results concerning the calculation of the variance of the Steins risk estimate are also provided in this work. Simulations carried out on natural images show the good performance of our method with respect to conventional wavelet-based restoration methods.

Vector-lifting schemes for lossless coding and progressive archival of multispectral images

In this paper, a nonlinear subband decomposition scheme with perfect reconstruction is proposed for lossless and progressive coding of multispectral images. The merit of this new scheme is to exploit efficiently the spatial and the spectral redundancies contained in the multispectral images related to a scene of interest. Besides, the proposed method is suitable for telebrowsing applications. Experiments carried out on real scenes allow to assess its performances. The simulation results demonstrate that our approach leads to improved compression performances compared with currently used lossless coders.

A hierarchical Bayesian model for frame representation

In many signal processing problems, it is fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyperparameters characterizing the probability distribution of the frame coefficients. This problem is difficult since in general the frame synthesis operator is not bijective. Consequently, the frame coefficients are not directly observable. This paper introduces a hierarchical Bayesian model for frame representation. The posterior distribution of the frame coefficients and model hyperparameters is derived. Hybrid Markov chain Monte Carlo algorithms are subsequently proposed to sample from this posterior distribution. The generated samples are then exploited to estimate the hyperparameters and the frame coefficients of the target signal. Validation experiments show that the proposed algorithms provide an accurate estimation of the frame coefficients and hyperparameters. Application to practical problems of image denoising in the presence of uniform noise illustrates the impact of the resulting Bayesian estimation on the recovered signal quality.

Vector Lifting Schemes for Stereo Image Coding

Many research efforts have been devoted to the improvement of stereo image coding techniques for storage or transmission. In this paper, we are mainly interested in lossy-to-lossless coding schemes for stereo images allowing progressive reconstruction. The most commonly used approaches for stereo compression are based on disparity compensation techniques. The basic principle involved in this technique first consists of estimating the disparity map. Then, one image is considered as a reference and the other is predicted in order to generate a residual image. In this paper, we propose a novel approach, based on vector lifting schemes (VLS), which offers the advantage of generating two compact multiresolution representations of the left and the right views. We present two versions of this new scheme. A theoretical analysis of the performance of the considered VLS is also conducted. Experimental results indicate a significant improvement using the proposed structures compared with conventional methods.

Two-dimensional non separable adaptive lifting scheme for still and stereo image coding

Many existing works related to lossy-to-lossless image compression are based on the lifting concept. However, it has been observed that the separable lifting scheme structure presents some limitations because of the separable processing performed along the image lines and columns. In this paper, we propose to use a 2D non separable lifting scheme decomposition that enables progressive reconstruction and exact decoding of images. More precisely, we focus on the optimization of all the involved decomposition operators. In this respect, we design the prediction filters by minimizing the variance of the detail signals. Concerning the update filters, we propose a new optimization criterion which aims at reducing the inherent aliasing artefacts. Simulations carried out on still and stereo images show the benefits which can be drawn from the proposed optimization of the lifting operators.

Copula-based statistical models for multicomponent image retrieval in thewavelet transform domain

In this paper, we are interested in multicomponent image indexing in the Wavelet Transform (WT) domain. More precisely, a WT is applied to each component then a suitable parametric model is retained for the distribution model of the wavelet coefficients. The parameters of this model are chosen as the salient features of the image content. The contribution of this work consists in choosing a parametric model which reflects the main dependencies existing between the resulting coefficients consisting of cross-component correlations and inter-scale similarities. The copula concept is introduced for building an appropriate statistical model of all the wavelet coefficients. Once the signatures are extracted, the retrieval procedure associated with a given query image is performed. Experimental results indicate that considering simultaneously the cross-component and the inter-scale correlation drastically improves the retrieval performances of the wavelet-based retrieval system.

Adaptive lifting for multicomponent image coding through quadtree partitioning

The objective of this paper is the design of adaptive quincunx lifting schemes for lossless compression of multiband images. More precisely, the operators of the lifting scheme are modified according to the local activity of the multivariate input signal. To this respect, a block-based adaptive strategy is adopted: the image is partitioned into a quadtree structure and a couple of optimal operators is assigned to each resulting volumetric segmented block. Our main contribution consists of a suitable quadtree partitioning rule that takes into account simultaneously the spatial and spectral redundancies. Simulations performed on real satellite images show that the proposed adaptive method outperforms the conventional non-adaptive lifting schemes.